SOLUTION: can you please prove this identity (sin x - tan x)(cos x - cot x)=(cos x -1)(sin x -1)

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Question 434537: can you please prove this identity
(sin x - tan x)(cos x - cot x)=(cos x -1)(sin x -1)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
(sin x - tan x)(cos x - cot x)=(cos x -1)(sin x -1)
start with left side
(sinx-sinx/cosx)(cosx-cosx/sinx)
((cosxsinx-sinx)/cosx)((cosxsinx-cosx)/sinx)
(sinx(cosx-1)(cosx(sinx-1))/cosxsinx
(cosx-1)(sinx-1)
verified: left side=right side